双向链表上快速排序的Python程序

以下是数组快速排序的典型递归实现。该实现使用最后一个元素作为枢轴。

Python3

"""A typical recursive implementation of Quicksort for array """
   
""" This function takes last element as pivot, 
   places the pivot element at its correct 
   position in sorted array, and places all 
   smaller (smaller than pivot) to left of
   pivot and all greater elements to right 
   of pivot 
"""
  
"""
 i --> is the first index in the array
 x --> is the last index in the array
 tmp --> is a temporary variable for swapping values (integer)
"""
# array arr, integer l, integer h
def  partition (arr, l, h):
    x = arr[h]
    i = (l - 1)
    for j in range(l, h):
        if (arr[j] <= x):
            i +=1
            tmp = arr[i]
            arr[i] = arr[j]
            arr[j] = tmp
  
    tmp = arr[i + 1]
    arr[i + 1] = arr[h]
    arr[h] = tmp
    return(i + 1)
  
"""
A --> Array to be sorted,
l --> Starting index, 
h --> Ending index
"""
  
# array A, integer l, integer h
def quickSort(A, l, h):
    if (l < h):
        p = partition(A, l, h) # pivot index
        quickSort(A, l, p - 1) # left
        quickSort(A, p + 1, h) # right
  
# This code is contributed by humphreykibet.

我们可以对链表使用相同的算法吗？
以下是双向链表的 C++ 实现。这个想法很简单，我们首先找出指向最后一个节点的指针。一旦我们有了指向最后一个节点的指针，我们就可以使用指向链表的第一个和最后一个节点的指针对链表进行递归排序，类似于上面传递第一个和最后一个数组元素的索引的递归函数。链表的分区函数也类似于数组的分区。它不是返回枢轴元素的索引，而是返回一个指向枢轴元素的指针。在下面的实现中，quickSort() 只是一个包装函数，主要的递归函数是_quickSort()，类似于数组实现的quickSort()。

Python3

# A Python program to sort a linked list using Quicksort
head = None
  
# a node of the doubly linked list
class Node:
    def __init__(self, d):
        self.data = d
        self.next = None
        self.prev = None
  
# A utility function to find last node of linked list
def lastNode(node):
    while(node.next != None):
            node = node.next;
    return node;
  
# Considers last element as pivot, places the pivot element at its
#   correct position in sorted array, and places all smaller (smaller than
#   pivot) to left of pivot and all greater elements to right of pivot 
def partition(l, h):
  
    # set pivot as h element
        x = h.data;
           
        # similar to i = l-1 for array implementation
        i = l.prev;
          
        j = l
          
        # Similar to "for (int j = l; j <= h- 1; j++)"
        while(j != h):
            if(j.data <= x):
                
                # Similar to i++ for array
                i = l if(i == None) else i.next;
  
                temp = i.data;
                i.data = j.data;
                j.data = temp;
            j = j.next
                          
        i = l if (i == None) else i.next;  # Similar to i++
        temp = i.data;
        i.data = h.data;
        h.data = temp;
        return i;
  
# A recursive implementation of quicksort for linked list 
def _quickSort(l,h):
    if(h != None and l != h and l != h.next):
            temp = partition(l, h);
            _quickSort(l,temp.prev);
            _quickSort(temp.next, h);
          
# The main function to sort a linked list. It mainly calls _quickSort()
def quickSort(node):
    
    # Find last node
        head = lastNode(node);
           
        # Call the recursive QuickSort
        _quickSort(node,head);
  
# A utility function to print contents of arr
def printList(head):
    while(head != None):
            print(head.data, end=" ");
            head = head.next;
          
# Function to insert a node at the beginning of the Doubly Linked List 
def push(new_Data):
    global head;
    new_Node = Node(new_Data);     # allocate node 
           
    # if head is null, head = new_Node
    if(head == None):
        head = new_Node;
        return;
      
    # link the old list off the new node 
    new_Node.next = head;
          
    # change prev of head node to new node 
    head.prev = new_Node;
          
    # since we are adding at the beginning, prev is always NULL 
    new_Node.prev = None;
          
    # move the head to point to the new node 
    head = new_Node;
  
# Driver program to test above function 
push(5);
push(20);
push(4);
push(3);
push(30);
  
  
print("Linked List before sorting ");
printList(head);
print("
Linked List after sorting");
quickSort(head);
printList(head);
  
# This code is contributed by _saurabh_jaiswal

输出 ：

Linked List before sorting
30  3  4  20  5
Linked List after sorting
3  4  5  20  30

时间复杂度：上述实现的时间复杂度与数组的 QuickSort() 的时间复杂度相同。在最坏情况下需要 O(n^2) 时间，在平均和最佳情况下需要 O(nLogn)。最坏的情况发生在链表已经排序时。
我们可以为链表实现随机快速排序吗？
只有当我们可以选择一个固定点作为枢轴（如上述实现中的最后一个元素）时，才能为链表实现快速排序。随机快速排序无法通过选择随机枢轴有效地为链表实现。

有关详细信息，请参阅双向链表上有关快速排序的完整文章！